# ANOVA - when homogeneity of variance is violated

My data was a repeated measurement (3-4 measuring times) with one fixed factor (4 doses) and nested (Please find an example below).

I would like to ran ANOVA but the assumption of homogeneity of variance was violated for some of the measuring times (e.g. Day1). Transformation of data did not fix the problem, what test could I use? Should I use Welch–Satterthwaite adjustment for F value, or use generalized mixed model or ran non-parametric test? I saw these three methods were use when Levene test is significant, or any other method would be better?

Thank you deeply for all the generous help!

ID   Location Dose  Day1    Day 3    Day 7
1     A       0.1    2.3     3.1      3.07
2     A       0.1    2.02    2.9      3.02
3     B       0.1    2.5     3.5      5.12
4     B       0.1    2.3     4.05     5.07
5     C       0.2    2.2     6.1      6.55
6     C       0.2    2.5     3.1      3.07
7     D       0.2    2.1     5.1      5.25
8     D       0.2    2.4     3.3      4.07


Since you assume is homogeneity is violated, data transformation is only alternative to minimize the variation in the data obtained. I have this kind of same problem like you, and I tried the Generalized Linear mixed model with dependent follow to poisson distribution. For your case, I think the dependent follow any distribution such exponential or else, just see the pattern. Good luck..

Here is the sample to analyze GLMM using R

• I am using SPSS Linear Mixed Model to analyze my data and wonder do I need to keep the assumption of homogeneity of variance. I heard that GLMM do not need to keep this assumption, is it true? Thanks a lot.
– Kam
Oct 18, 2014 at 6:30
• yes u right, GLMM do not assumes the residual follow gaussian distribution. SPSS also very cool to run the result as like as R. You can do as comfort for u. any way do not forget to accept the answer. Thanks. Oct 18, 2014 at 8:20
• Thank you! I am a bit confuse with Linear Mixed Model, do I need to keep the homogeneity of variance assumption? Seemed that LMM allows defining the covariance structure (R Matrix)? I am not sure about checking homogeneity of variance as well, I ran Levene test on my dependent variable at each time point. But others seemed to plot predicted vs residual or do a Q-Q plot? If I do Q-Q plot, should I use the residuals generated from the model or use dependent variables? Thank you very much!
– Kam
Oct 18, 2014 at 10:18
• Here is the answer, Q: I am a bit confuse with Linear Mixed Model, do I need to keep the homogeneity of variance assumption? A: both homogeneity and normal distribution is not assumes in GLMM. Q: If I do Q-Q plot, should I use the residuals generated from the model or use dependent variables? A: use the residual instead of dependent variables Oct 18, 2014 at 14:14
• Sorry to have asked so many question. Just one thing wanna to make sure, is it Linear mixed model(lmm) the same as generalised linear mixed model(glmm) that don't need both homogeneity and normal distribution? Really thank you so much!!
– Kam
Oct 19, 2014 at 0:26